Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of sin(x)*dx/x
Integral of 1/sqrt(x^2+1)
Integral of x^3*ln(x)
Integral of x*ln(x+1)dx
Identical expressions
(three x^ two)*(e^-x^3)
(3x squared ) multiply by (e to the power of minus x cubed )
(three x to the power of two) multiply by (e to the power of minus x cubed )
(3x2)*(e-x3)
3x2*e-x3
(3x²)*(e^-x³)
(3x to the power of 2)*(e to the power of -x to the power of 3)
(3x^2)(e^-x^3)
(3x2)(e-x3)
3x2e-x3
3x^2e^-x^3
(3x^2)*(e^-x^3)dx
Similar expressions
(3x^2)*(e^+x^3)

Solving integrals/ (3x^2)*(e^-x^3)

Integral of (3x^2)*(e^-x^3) dx

The solution

You have entered [src]

 oo             
  /             
 |              
 |          3   
 |     2  -x    
 |  3*x *e    dx
 |              
/               
2

$$\int\limits_{2}^{\infty} 3 x^{2} e^{- x^{3}}\, dx$$

Integral(3*x^2/E^(x^3), (x, 2, oo))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int 3 x^{2} e^{- x^{3}}\, dx = 3 \int x^{2} e^{- x^{3}}\, dx$
1. Let $u = e^{- x^{3}}$ .
  
  Then let $du = - 3 x^{2} e^{- x^{3}} dx$ and substitute $- \frac{du}{3}$ :
  
  $\int \frac{1}{9}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- \frac{1}{3}\right)\, du = - \frac{\int 1\, du}{3}$
    1. The integral of a constant is the constant times the variable of integration:
      
      $\int 1\, du = u$
    So, the result is: $- \frac{u}{3}$
  Now substitute $u$ back in:
  
  $- \frac{e^{- x^{3}}}{3}$
So, the result is: $- e^{- x^{3}}$
Add the constant of integration:

$- e^{- x^{3}}+ \mathrm{constant}$

The answer is:

$- e^{- x^{3}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                       
 |                        
 |         3             3
 |    2  -x            -x 
 | 3*x *e    dx = C - e   
 |                        
/

$$-e^ {- x^3 }$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

 -8
e

$$3\,\left({{e^ {- 8 }}\over{3}}-{{e^ {- {\it oo}^3 }}\over{3}} \right)$$

 -8
e

$$e^{-8}$$

Упростить

The graph

Use the examples entering the upper and lower limits of integration.

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (3x^2)*(e^-x^3) dx

Limits of integration:

The graph:

Piecewise:

The solution